Finite Group Databasebeta

← #13069951

Subgroups — #13069951

Order 1408.

250 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 91 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#125C211yesmaximal, characteristic
2C2×#66872C211yesmaximal, characteristic
3C2×#66871C211yesmaximal, characteristic
4#10622541C211yesmaximal, characteristic
5#10622167C211yesmaximal, characteristic
6#10622167C211yesmaximal, characteristic
7#10622162C211yesmaximal, characteristic
8C11×#125—22no—
9C11×#125—22no—
10C2×C11×C4⋊C4—21no—
11C2×C11×C4⋊C4—21no—
12C2×C11×C4⋊C4C2211yescharacteristic
13C2×C11×C4⋊C4C2211yescharacteristic
14C2×C42×C11C2211yescharacteristic
15C2×C4⋊Dic11C2211yescharacteristic
16C2×C4⋊Dic11C2211yescharacteristic
17C2×Dic11⋊C4—21no—
18C22×C11⋊C8C2211yescharacteristic
19C22×C11⋊C8C2211yescharacteristic
20C11⋊#95—21no—
21#66872—22no—
22#66871—22no—
23C22×C4×C11—21no—
24C22×C4×C11—21no—
25C22×C4×C11D411yescharacteristic
26C22×C4×C11D411yescharacteristic
27C22×C4×C11C2311yescharacteristic
28C22×Dic11—21no—
29C22×Dic11—21no—
30C11×C4⋊C4—24no—
31C11×C4⋊C4—24no—
32C11×C4⋊C4—21no—
33C11×C4⋊C4—21no—
34C11×C4⋊C4D412yes—
35C11×C4⋊C4D412yes—
36C42×C11—21no—
37C42×C11—21no—
38C4⋊Dic11—21no—
39C4⋊Dic11—21no—
40C4⋊Dic11—21no—
41C4⋊Dic11Q812yes—
42Dic11⋊C4—42no—
43C2×C11⋊C8—21no—
44C2×C11⋊C8—21no—
45C2×C11⋊C8—21no—
46C2×C11⋊C8—21no—
47C2×C11⋊C8Q812yes—
48C2×C11⋊C8Q812yes—
49#2059—111nomaximal, Sylow
50C23×C11C2×D411yescharacteristic
51C2×C4×C11—21no—
52C2×C4×C11—21no—
53C2×C4×C11—22no—
54C2×C4×C11—22no—
55C2×C4×C11—21no—
56C2×C4×C11—21no—
57C2×C4×C11—21no—
58C2×C4×C11—21no—
59C2×C4×C11—41no—
60C2×C4×C11—41no—
61C2×C4×C11—41no—
62C2×C4×C11—41no—
63C2×C4×C11C2×D411yescharacteristic
64C2×C4×C11C2×D411yescharacteristic
65C2×C4×C11C2×Q811yescharacteristic
66C2×C4×C11C2×Q811yescharacteristic
67C2×C4×C11C2×Q811yescharacteristic
68C2×C4×C11#4111yescharacteristic
69C2×Dic11—22no—
70C2×Dic11—41no—
71C2×Dic11—41no—
72C2×Dic11—41no—
73C2×Dic11—41no—
74C2×Dic11—41no—
75C11⋊C8—22no—
76C11⋊C8—22no—
77C2×#125D1111yescharacteristic
78C2×#107—111no—
79C2×#106—111no—
80#389—111no—
81#340—111no—
82#340—111no—
83#336—111no—
84C22×C11#12011yescharacteristic
85C22×C11C22⋊Q811yescharacteristic
86C22×C11C4⋊Q811yescharacteristic
87C22×C11#13511yescharacteristic
88C22×C11#13511yescharacteristic
89C22×C11AGL(1,ℤ/8)11yescharacteristic
90C22×C11#13711yescharacteristic
91C4×C11—41no—
92C4×C11—42no—
93C4×C11—41no—
94C4×C11—42no—
95C4×C11C22⋊Q811yescharacteristic
96C4×C11C22⋊Q811yescharacteristic
97C4×C11C4⋊Q811yescharacteristic
98C4×C11C4⋊Q811yescharacteristic
99Dic11—42no—
100Dic11—81no—
101C22×C8—111no—
102C22×C8—111no—
103#125—22no—
104#125—22no—
105C2×C4⋊C4—21no—
106C2×C4⋊C4—21no—
107C2×C4⋊C4—111no—
108C2×C4⋊C4—111no—
109C2×C4⋊C4—221no—
110C2×C4⋊C4C2×D1111yescharacteristic
111C2×C4⋊C4C2×D1111yescharacteristic
112C2×C42C2×D1111yescharacteristic
113#107—222no—
114#106—222no—
115#95—221no—
116C2×C11#39511yescharacteristic
117C2×C11#44911yescharacteristic
118C2×C11#45211yescharacteristic
119C2×C11#47811yescharacteristic
120C2×C11#47911yescharacteristic
121C2×C11#49911yescharacteristic
122C2×C11#50111yescharacteristic
123C22×C4—21no—
124C22×C4—21no—
125C22×C4—221no—
126C22×C4—221no—
127C22×C4C22⋊D1111yescharacteristic
128C22×C4C22⋊D1111yescharacteristic
129C22×C4C22×D1111yescharacteristic
130C2×C8—112no—
131C2×C8—112no—
132C2×C8—221no—
133C2×C8—221no—
134C2×C8—221no—
135C2×C8—221no—
136C4⋊C4—24no—
137C4⋊C4—24no—
138C4⋊C4—21no—
139C4⋊C4—21no—
140C4⋊C4—112no—
141C4⋊C4—221no—
142C4⋊C4—221no—
143C4⋊C4—221no—
144C4⋊C4—442no—
145C4⋊C4C22⋊D1112yes—
146C4⋊C4C22⋊D1112yes—
147C42—21no—
148C42—21no—
149C11#205911yescharacteristic, complemented, Sylow
150C23C2×C22⋊D1111yescharacteristic
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—222no—
164C2×C4—441no—
165C2×C4—441no—
166C2×C4—441no—
167C2×C4—441no—
168C2×C4—441no—
169C2×C4Q8×D1111yescharacteristic
170C2×C4Q8×D1111yescharacteristic
171C2×C4Q8×D1111yescharacteristic
172C2×C4#434311yescharacteristic
173C2×C4C2×C22⋊D1111yescharacteristic
174C2×C4C2×C22⋊D1111yescharacteristic
175C8—222no—
176C8—222no—
177C22#6699711yescharacteristic
178C22#6699911yescharacteristic
179C22#6700211yescharacteristic
180C22#6700311yescharacteristic
181C22#6700311yescharacteristic
182C22#6700411yescharacteristic
183C22#6700611yescharacteristic
184C4—41no—
185C4—42no—
186C4—41no—
187C4—42no—
188C4—442no—
189C4—881no—
190C4#6699711yescharacteristic
191C4#6699711yescharacteristic
192C4#6699911yescharacteristic
193C4#6699911yescharacteristic
194C2#1062267611yescharacteristic
195C2#1062267711yescharacteristic
196C2#1062267811yescharacteristic
197C2#1062267911yescharacteristic
198C2#1062284211yescharacteristic
199C2#1062285111yescharacteristic
200C2#1062285211yescharacteristic
subgroupG/H
centerC23C2×C22⋊D11
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC2×C11×#125C2
socle, prime radicalC23×C11C2×D4
hypercenterC2×#125D11
hypocenterC11#2059
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#125

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
149. C11#2059semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C11×#1252
C2×#668722
C2×#668712
#106225412
#106221672
#106221622
#205911